vCenter has a ton of logs in /var/log
on vCenter Server Server Appliance, these are the ones I find the most useful.
In order to search the logs directly, turn SSH on from VCSA:
You must log in to https://vcenter.example.com:5480/
as administrator@vsphere.local and not your Active Directory user.
Access > Edit > tick both Enable BASH Shell & Enable SSH Login
Login: ssh root@vcenter.example.com
Go into the shell by typing shell
Now you can parse the logs.
grep "username" /var/log/vmware/vpxd/vpxd.log
grep "error" /var/log/vmware/vpxd/vpxd.log
grep "warning" /var/log/vmware/messages
grep "cert" /var/log/vmware/messages
Turn off shell & SSH access when finished.